Amid a bitter debate over taming the federal deficit, the political parties are in rare agreement on a need to curb the nation’s spending on health care — and on Medicare most of all.

But with Democrats on the Hill vilifying a plan by House Republicans to privatize Medicare, lawmakers are stalemated over how to curb costs in the program, which is forecast to be the biggest contributor to future federal deficits.

Despite the lack of political momentum, a few Democratic health-policy experts contend that changes are needed quickly, and on Friday, Sen. Joseph I. Lieberman of Connecticut, an independent, put forth his own plan, lamenting the “partisan pugilism.” For the most part, Democratic health-policy analysts support a patchwork of older ideas, such as raising retirement ages, making moderate use of private subsidies or setting higher prices for wealthy participants.

The most optimistic liberal health-policy experts contend that Medicare costs will slow because of changes embedded in last year’s law to overhaul the health-care system. Those are forecast to save about $550 billion by the end of the decade, in part by reducing payments to some private health plans or by delivering care more efficiently.

“In many ways, the Democrats sort of shot their wad on the Affordable Care Act,” said Marilyn Moon, senior vice president and director of the health program at the American Institutes for Research. “We have to see how far it takes us before we start a lot of other stuff.”

The top official overseeing Medicare for the Obama administration, Donald M. Berwick, is a cheerleader for the notion that coordinating care saves money. But even he acknowledges that the “tempo” of improvements under the law may not be fast enough.

There are political obstacles to almost all the other ideas under discussion among Democrats, some of which have been promoted — unsuccessfully — in the past. “The reason why they aren’t law now is they have a constituency and at least semi-credible arguments that makes adding them to the pot quite challenging,” said Chris Jennings, who was the Clinton administration’s top health-care adviser.

Nonetheless, financial pressures on the program, which is a lifeline to health care for 48 million Americans 65 and older, are intensifying. Medicare’s cost per person is the lowest in years, but its finances are being upturned by the aging baby boomers, increasing life spans and the ballooning cost of care. The program’s spending is likely to increase from $519 billion last year to $929 billion by the end of the decade, according to congressional budget analysts. And the trust fund that pays for Medicare patients’ hospital bills is predicted to run short of money by 2024, five years earlier than predicted a year ago, according to trustees.

Among the few Democrats who talk openly about an immediate need to address this fiscally treacherous future is Alice M. Rivlin, a senior fellow at the Brookings Institution and former director of the Congressional Budget Office. She argues that waiting until after the 2012 presidential election — as many Democrats would prefer — “is too late. I don’t think we have two years to play around with this.”

Rivlin favors a compromise that would keep the original fee-for-service version of Medicare, created in 1965, and add an alternative giving older Americans government subsidies to help pay for private health-care plans — a more moderate version of the proposal advanced by House Budget Committee Chairman Paul Ryan (R-Wis.).

“The question,” Rivlin said, “is whether Ryan has so poisoned the well that Democrats won’t even talk about” any plan that includes premium supports.

The idea on which Democrats might be most likely to agree, policy experts say, would build on a rule in the health-care law that will give a controversial new board the power to recommend cuts if Medicare spending grows 1 percent faster than the gross domestic product. This spring, as part of his plan to lower the deficit, President Obama proposed that the “cap” be tightened — to 0.5 percent.

The idea could prove popular, because it defers specific cuts. “The challenge comes when the specific savings would have to be put on the table,” said Tricia Neuman, director of the Kaiser Family Foundation’s Medicare Policy Project.

Another possibility would be to charge wealthy participants more — a trend that has begun. This year, for the first time, about 1.2 million of the 28 million people who buy Medicare’s prescription drug benefits are having to pay more for them. And the proportion of older Americans required to pay higher premiums for coverage of doctor visits is predicted to increase from 5 percent to 14 percent by the end of the decade.

But higher charges have a limited ability to generate extra money, because few Americans in the program are wealthy. Half have incomes of $22,000 a year or less, Neuman said.

Policy experts are similarly skeptical that raising the eligibility age would save much. Increasing the age to 67, Moon said, would affect about 5 percent of the people in the program but save just 2 percent of the costs, because that age group tends to need less care than older people. Besides, Rivlin said, a lot of people in that age range are no longer working, so they wouldn’t be able to get coverage through a job, and they are not poor enough to join Medicaid. “So what do you do with those people?” Rivlin asked.

Another idea would place restrictions on supplemental insurance, known as Medigap. Now, some Medigap policies cover care right from the start. Researchers have suggested that requiring patients to pay a deductible up front might deter them from getting care they might not need. A recent presidential commission on the deficit, on which Rivlin served, recommended the idea and projected it would save $49 billion over the first five years. Others say that, to be effective, the deductible would have to be very high — inevitably producing loud complaints from Medicare patients and the insurance industry.

Similarly, the pharmaceutical industry is against a proposal that both the White House and the deficit commission have endorsed: paying lower prices for medicine needed by 9 million poor, older Americans who qualify for both Medicare and Medicaid.

Taken together, said Andrew L. Stern, a member of the fiscal commission and former president of the Service Employees International Union, the ideas mean that “you have sort of the boldness of Ryan and the timidity of the alternative. . . . They will make things better but not solve the problem . . . [they] put the cancer in remission a little bit longer.”